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As I was working on this paper https://hal.science/hal-00319947/document by Emmanuel Gobet, I came across this paragraph that says to price a barrier option on (for example) two correlated assets, you can derive two biased estimators that acts like bounds and average them to estimate the price of the option. This looks amazing since you do not really need to quantify the correlation between the two assets, but how would one price a multi-asset option in the general case? As I only have experience with pricing for a single asset, I was wondering what would be the industry standard in this regard. My first idea would be to use MC simulations with (for example again) local vol models calibrated on each of the assets and using correlated increments. But how could one estimate the correlation here ? Could you use vanilla prices to estimate a sort of implied correlation between the two assets? Or using an index ? I would be happy to discuss this or if you could provide me with some references. Thanks for your time !

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